Answered: Statistics Question

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question #5:

16.

Let $μ_{1}$ is defined as the population mean of the lower class participants, and $μ_{2}$ is defined as the population mean of the upper class participants. The claim of the test is that there is a significant mean difference between the two economic populations. The hypothesis is,

Null hypothesis:

$H_{0} : μ_{1} - μ_{2} = 0$

Alternative hypothesis:

$H_{1} : μ_{1} - μ_{2} \neq 0$

The pooled variance is,

$\begin{array}{rcl} s_{p}^{2} & = & \frac{S S_{1} + S S_{2}}{n_{1} + n_{2} - 2} \\ = & \frac{11.91 + 9.21}{12 + 12 - 2} \\ = & \frac{21.12}{22} \\ = & 0.96 \end{array}$

The test statistic is,

$\begin{array}{rcl} t & = & \frac{M_{1} - M_{2}}{\sqrt{s_{p}^{2} (\frac{1}{n_{1}} + \frac{1}{n_{2}})}} \\ = & \frac{5.2 - 4.3}{\sqrt{0.96 (\frac{1}{12} + \frac{1}{12})}} \\ = & \frac{0.9}{0.4} \\ = & 2.25 \end{array}$

The test statistic is 2.25.

Computation of critical value:

The critical value of t-distribution at 22 degrees of freedom can be obtained using the excel formula “=T.INV.2T(0.05,22)”. The critical value is 2.0739.

Decision rule:

If test statistic > critical value, then reject the null hypothesis. Otherwise, do not reject the null hypothesis.

Conclusion:

The test statistic (2.25) is greater than the critical value (2.0739).

Based on decision rule, reject the null hypothesis.

Thus, there is sufficient evidence to conclude that there is a significant mean difference between the two economic populations.